Local mean NPMR, Gaussian weights used to relate lichen biomass to
stand structure and topography. Based on the response surfaces observed with NPMR, they
chose final models of three types: NPMR, nonlinear regression, and multiple linear
regression.

quantitative (species richness in relation to
geography and community ordination scores)

Local linear NPMR, Gaussian weights. Compared fit of species
richness to four different sets of predictors: topographic+geographic, vascular plants,
the combination of the two preceding sets, and community ordination scores.

Local mean NPMR, Gaussian weights. Stepwise selection of predictors
representing climate and forest structure; randomization test. Predictors were selected
from a pool of 15 variables and evaluated with a randomization test. Models were used to
generate predictions based on future climate scenarios.

Local mean NPMR, Gaussian weights. Modeled species presence against
climatic predictors; included randomization tests and AUCs. They present NPMR models for
many species, depicted them geographically rather than response surfaces in the predictor
space.

Assessed the relative roles of age and habitat in creating and
maintaining species diversity. "The use of multiple overlapping data sets
[predictors] with NPMR and subsequent comparison permits complex interactions between
different variables to be teased out."

Local mean NPMR, Gaussian weights, modeling the density of many
bird species in relationship to numerous habitat factors. This paper gives a lucid
explanation of NPMR, three dimensional response surfaces, and some nice examples of
interacting nonlinear responses.

Local mean NPMR with Gaussian weights. Compared the performance of
Random Forests, Classification and Regression Trees, and NPMR using a large variety of 3D
response surfaces. They found: "The accuracy of each method depends on the threshold
strength and diagonality of the original data structure with each method differing in
degree of dependence (Fig. 4). The accuracy of most methods decreases as diagonality
increases and threshold strength decreases with the exception of NPMR with continuous
data... NPMR demonstrates the least variability (seen as quantile bars in Fig. 4) and the
greatest accuracy (seen as medians in Fig. 4) compared to the other methods for a given
response shape. The sensitivities of modeling methods to shape attributes of data
structure arises from features specific to each modeling method, which manifest in visual
differences of predicted surfaces for different shapes (Fig. 5). For our subsequent
analyses using real ecological data, we choose the most accurate and robust method we
test, NPMR."

Local linear and local mean NPMR, Gaussian weights. Modeled
abundance of three diatom species in relation to water quality variables. Includes a table
comparing fits for local linear and local mean models. In general, the fits were slightly
higher for local linear models.

Local mean NPMR, Gaussian weights, used to model species presence
in relation to habitat and geographic variables at two scales. "NPMR generally
performs well at both spatial scales and that distributions of non-indigenous species are
predicted as well as those of native species."

Local mean NPMR with Gaussian weights. "NPMR was compared with
logistic regression (LR) by building reduced models from variables selected as best by
NPMR and full models from variables identified as significant with a forward stepwise
process and further manual testing. LogB was used to select models with the highest
predictive capability. NPMR models were less complex and had higher predictive capability
than LR for all modeling approaches. Spatial coordinates were among the most powerful
predictors and the modeling approach with physiographic and stand structural variables
together was the most improved relative to the average frequency of occurrence. GIS
probability maps produced with the application of the physiographic models showed good
spatial congruence between high probability values and plots that contained CLUN. NPMR
proved to be a reliable probability modeling and mapping tool that could be used as the
analytical link between monitoring and quantifying the status and trends of vegetation
resources."